The Times and Sunday Times have sharply increased their readership in Scotland by using voucher promotions, bundled offers and bulk distribution.
The daily title saw average Scottish circulation up to 24,400 in March.
That puts it ahead of the most recent figures for its rival, The Scotsman.
The Edinburgh-based title, in the latest figures available, had average daily circulation of 22,700 between July and December last year. Of them, only 14,200 were sold at full price.
A tenth of its circulation was in multiple copies, distributed in hotels and at airports.
The figures show how newspaper marketing and promotions are changing the shape of the industry, as conventional newsagent sales decline.
Those papers sold below full price are deemed less valuable to the industry, not only because of the lack of cover price revenue but also because advertisers do not see giveaways as reaching people with as great a commitment to read articles and see adverts.
Among British titles, The Times and Sunday Times have led the way in putting their online journalism behind a pay-wall. These have been heavily promoted with special offers, currently including free membership of the National Trust for Scotland and student deals.
The Sunday Times jettisoned most of its reporting staff in Scotland and has a limited amount of Scottish content. The Times continues to employ journalists from its Glasgow office and covering Holyrood, and to produce a Scottish edition.
London-based national titles report their figures separately from most Scottish newspapers, including The Scotsman, and more often. The monthly figures for March show that just under 15,000 of The Times' sales in Scotland were at full price - just ahead of The Scotsman average last year.
According to industry figures compiled by the Audit Bureau of Circulation, that was an 8% rise on the average for March 2015.
Voucher-based sales fell 11% to 3,500, while multiple circulation was up six-fold to 5800.
The Sunday Times had full price sales of 36,000 in Scotland, to which it added 4900 through subscriptions and 5500 through multiple distribution.
Innovative marketing also helped The Daily Telegraph to turn around a long term decline across Britain, by adding 8000 bulk sales.
In Scotland, the Telegraph added 4% full-price sales since March of last year, to reach a daily average of 8300, while voucher-based sales fell 4% since last year to 7,600.
The bigger-selling daily titles in Scotland saw full-price sales for the market leader, The Sun, dip below 200,000. It has fallen by 11% in the year to March.
The Sun had additional circulation of 23,000 through lower-price sales and giveaways.
Its rival, the Daily Record, based in Glasgow, saw full-price sales slip 13% over the past year, to below 168,000. Of them, all but 6000 were sold at full price.
The Daily Mail had average Scottish full-price sales of 83,000 last month, down 4% in a year. In addition, it had a circulation of 3,000 at less than full price or free.
In Scotland's weekly market for newspapers, the Sunday Mail registered 176,500 average full-price sales last month, down 14% in a year, and with fewer than 4000 giveaways.
The Sunday Post sold 121,000 at full price, a decline of 11%.
The circulation figures for The Herald over the second half of last year were just above 32,000, almost all of them sold at full price, and down 13% on July to December of 2014.
The decline was less steep for the Press and Journal, based in Aberdeen, down 6% in a year at 56,400 average daily sales.
Its sister paper in Dundee, the Courier, reported circulation down 8% to 43,000, with fewer than 500 of each title being given away.